量子态区分中的关键问题研究

Local distinguishability of orthogonal quantum states is an important research content of quantum nonlocality theory, and is also one of burning problems in quantum information theory. This project intends to solve some key theoretical problems in quantum state discrimination and explore its application in quantum communication protocols. The main research contents include the following three aspects. Firstly, we study the conditions needed to locally distinguish orthogonal quantum states, and present the general determination conditions. Secondly, with the help of one low-dimensional entangled state or multiple copies low-dimensional entangled states, we design a protocol to locally distinguish orthogonal quantum states. Finally, based on entanglement resource to help distinguish orthogonal quantum states theory, we present a quantum communication protocol that saves resource and is safe. The research results of this project will enrich and improve the quantum nonlocality theory, promote the development of quantum information theory, and provide theoretical support for the application of the local discrimination theory in quantum information processing.

正交量子态的局域区分性是量子非局域性理论中的重要研究内容，也是量子信息技术中的研究热点之一。本项目拟解决量子态区分中的若干关键性理论问题，并探索其在量子通信协议中的应用。主要研究内容包括以下三个方面：研究局域区分正交量子态所需要的条件，给出一般性的判定条件；在一个低维纠缠态或多拷贝低维纠缠态的帮助下，设计局域区分正交量子态的协议；基于纠缠资源帮助区分正交量子态理论，设计出节省资源并且安全的量子通信协议。本项目的研究成果将丰富和完善量子非局域性理论，促进量子信息理论的发展，同时也为局域区分理论在量子信息处理中的应用提供理论支持。

在量子信息处理中，量子纠缠和量子非局域性都是非常重要的基础理论内容，而正交量子态的局域区分性是探索其关系的有效方法之一。本项目研究了局域区分正交量子态的条件、纠缠辅助区分正交量子态，并探索了其在量子通信中的应用，取得了重要成果：设计了两种不同的纠缠辅助区分两方量子系统中一类不可扩展直积基的协议；设计出两方量子系统中纠缠辅助区分一类正交直积态的协议；设计出少量的纠缠资源帮助区分三方甚至多方量子系统中具有非局域性的正交直积态集合的协议；构造了多方量子系统中具有强非局域性的最大纠缠态；设计出两类新颖的匿名否决协议，取得了较好的进展。本项目的研究成果丰富和完善了量子非局域性理论，扩展了纠缠在量子信息处理中的作用，促进了量子信息理论的发展，并为今后的实际应用提供了理论支持。